High Energy Physics - Theory

Title:
What is the Simplest Quantum Field Theory?

Abstract: Conventional wisdom says that the simpler the Lagrangian of a theory the
simpler its perturbation theory, but an increased understanding of the
structure of the S-matrix in gauge theories and gravity has been pointing to
the opposite conclusion. In this paper we suggest that N=8 SUGRA has the
simplest interacting S-matrix in 4D. Using Grassmann coherent states for
external particles shows that amplitudes with maximal SUSY are smooth objects,
with the action of SUSY manifest. We show that all tree amplitudes in N=4 SYM
and N=8 SUGRA vanish at (supersymmetric) infinite complex momentum, and can
thus be determined by recursion relations. We also identify the action of the
non-linearly realized E_{7(7)} symmetry of N=8 SUGRA on scattering amplitudes.
We give a simple discussion of the structure of 1-loop amplitudes in any QFT,
in close parallel to recent work of Forde, showing that the coefficients of
scalar "triangle" and "bubble" integrals are determined by the "pole at
infinite momentum" of tree amplitude products appearing in cuts. The on-shell
superspace for maximal SUSY makes it easy to compute the multiplet sums that
arise in these cuts, leading to a simple proof of the absence of triangles and
bubbles at 1-loop. We also argue that rational terms are absent. This
establishes the recent conjecture that 1-loop amplitudes in N=8 SUGRA have only
scalar box integrals, just as N=4 SYM. It is natural to conjecture that with
maximal SUSY, amplitudes are completely determined by their leading
singularities even beyond tree- and 1-loop level; this would directly imply the
perturbative finiteness of N=8 SUGRA. The remarkable properties of scattering
amplitudes call for an explanation in terms of a "weak-weak" dual formulation
of QFT, a holographic dual of flat space.